Arithmetic infinite Grassmannians and the induced central extensions

TL;DR

This paper constructs families of Sato Grassmannians over arbitrary schemes, explores their determinant line bundles, and studies the central extensions they induce, broadening the understanding of infinite Grassmannians in algebraic geometry.

Contribution

It introduces a general construction of arithmetic infinite Grassmannians and analyzes the central extensions arising from their determinant line bundles over arbitrary base schemes.

Findings

Constructed families of Sato Grassmannians over arbitrary schemes.

Analyzed the determinant line bundles and associated central extensions.

Extended the theory of infinite Grassmannians to a more general algebraic setting.

Abstract

The construction of families of Sato Grassmannians, their determinant line bundles and the extensions induced by them are given. The base scheme is an arbitrary scheme.